Naslov
Spectral discretization errors in filtered subspace iteration

Autori
Gopalakrishnan, Jay ; Grubišić, Luka ; Ovall, Jeffrey

Izvornik
Mathematics of computation (0025-5718) 89 (2020), 321; 203-228

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
finite element approximations ; eigenvalue estimation ; error estimates

Sažetak
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation of an operator-valued contour integral of the resolvent. Resolvents on infinite-dimensional spaces are discretized in computable finite-dimensional spaces before the algorithm is applied. This study focuses on how such discretizations result in errors in the eigenspace approximations computed by the algorithm. The computed eigenspace is then used to obtain approximations of the eigenvalue cluster. Bounds for the Hausdorff distance between the computed and exact eigenvalue clusters are obtained in terms of the discretization parameters within an abstract framework. A realization of the proposed approach for a model second-order elliptic operator using a standard finite element discretization of the resolvent is described. Some numerical experiments are conducted to gauge the sharpness of the theoretical estimates.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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